The RXTE All Sky Monitor soft X-ray light curves of many
X-ray binaries show long-term intensity variations (a.k.a
"superorbital periodicities") that have been ascribed to
precession of a warped, tilted accretion disk around the
X-ray source. We have found that the excursion times between
X-ray minima in Cyg X-2 can be characterized as a series of
integer multiples of the 9.8 binary orbital period, (as
opposed to the previously reported stable 77.7 day single
periodicity, or a single modulation whose period changes
slowly with time). While the data set is too short for a
proper statistical analysis, it is clear that the length of
any given intensity excursion cannot be used to predict the
next (integer) excursion length in the series.

In the black hole candidate system LMC X-3, the excursion
times are shown to be related to each other by rational
fractions. We find that the long term light curve of the
unusual galactic X-ray jet source Cyg X-3 can also be
described as a series of intensity excursions related to
each other by integer multiples of a fundamental underlying
clock. In the latter cases, the clock is apparently not
related to the known binary periods. A unified physical
model, involving both an inclined accretion disk and a
fixed-probability disk disruption mechanism is presented,
and compared with three-body scattering results. Each time
the disk passes through the orbital plane it experiences a
fixed probability P that it will disrupt. This model has
testable predictions---the distribution of integers should
resemble that of an atomic process with a characteristic
half life. Further analysis can support or refute the model,
and shed light on what system parameters effectively set the
value of P.